An online capacitive densitometer has application to the measurement of bulk density and bulk flow of materials conveyed in a mixed phase medium.
Measurement of the density of materials conveyed in a duct or pipeline is needed in a variety of industrial bulk processing operations. In such industrial applications, solid materials in granular or powder form are transported in pipes or ducts by entrainment with a suitable fluid (gas or liquid). The solids may be raw material feedstock or intermediate products of chemical processes which may be run in batch mode or continuous mode. In continuous mode, optimum operation can require accurate control of the material feedrates. This, in turn, requires an accurate on-line measurement of the bulk density of the two-phase medium used to convey the solids.
For single-phase flow, such a measurement is not needed. Instead, the total flowrate can be inferred from an on-line measurement of the duct-averaged flow speed, obtainable by a variety of known and well-tested means. Presence of a second phase complicates measurement because (a) each phase may flow at a different velocity, especially for gas entrainment, (b) the distribution of phases through the duct may be highly inhomogeneous, (c) at desirable measurement sites, such as just before injection into a reactor, elevated temperatures and pressures may prevail, and (d) entrained solids flow constitutes a strongly erosive medium. Therefore, for measurement of a two phase flow, the following conditions apply: (a) At least two variables must be measured, (b) the measurement means should preferably be nonintrusive, and (c) accurate measurement implies accurate averaging over the duct, hence, a sensing device or scheme that senses the duct interior as uniformily as possible. In addition, it is desirable that the instrument can read absolutely and that it feature exceptionally good long-term stability.
Somewhat different specific considerations apply to gas-solid and liquid-solid media. For gas entrainment one typically finds solid volume fractions of less than 0.05, gas velocities of the order of 20 m/s and solid velocities that always have a considerable slip. Solid velocity measurement by cross correlation is readily feasible hence, an additional measurement of the medium bulk density .rho..sub.m or solid volume fractions .phi..sub.s will yield the solid feedrate m.sub.s, according to EQU m.sub.s =S v.sub.s .rho..sub.s .phi..sub.s ( 1)
where S=duct cross sectional area, v.sub.s =solid component velocity, `.sub.s =intrinsic density of the solid, .phi..sub.s =solid volume fraction. The bulk density is given by EQU .rho..sub.m =.rho..sub.s .phi..sub.s +.rho..sub.f (1-.phi..sub.s) (2)
where .rho..sub.f =fluid intrinsic density. Evidently, the second term is very small for a solid-gas medium. Gas entrainment features strongly inhomogeneous solids distributions across the duct, with bottom layers in long horizontal runs and enhanced central solids density elsewhere. Also, the flow regime is invariably highly turbulent.
Liquid-entrained solids conveyors typically feature solid volume fractions in excess of 0.6 which renders the medium highly viscous with a quasi-uniform solids distribution throughout the duct but a flow regime that ranges from transition to laminar/non-Newtonian. Velocity slip is negligible, with a medium velocity typically less than 5 m/s. Here, the bulk density is relatively accurately measurable even if the sensing efficiency is not quite uniform throughout the duct, while the velocity measurement becomes especially difficult.
A densitometer based upon capacitive sensing is ideally suited for making the type of measurement described above. Capacitive sensing is inherently non-invasive and only requires an insulating duct section. An on-line densitometer based on capacitive sensing is a device consisting of a set of electrodes or plates that encompass the medium. An electric field produced between the electrodes by an applied voltage senses the medium dielectric constant which amounts to the ratio of the measured capacity of the device in the presence and in the absence of the medium. Whereas conventional capacity sensors employed for densitometry or moisture measurement usually rely on calibration, there exist some well-established theoretical relations from which a connection can be made between the bulk (medium) dielectric constant and the solid volume fraction. These relations, together with known constants, furnish sufficient data to enable an absolute reading of the solid volume fraction.
In particular, the output signal voltage e.sub.m of an operational amplifier connected to a capacitor whose sensed volume is entirely filled with a two-component medium of the type discussed in the foregoing can be shown to be proportional to the capacity of said capacitor. The same capacitor filled entirely with the pure entraining fluid will yield a slightly different signal voltage, e.sub.f. Let the combination EQU (e.sub.m -e.sub.f)/e.sub.f =M (3)
then, if a fixed capacity C.sub.s exists in series with the capacitor that is filled with the medium, as for example, due to the presence of a dielectric wall between the capacitor plates and the medium, and if EQU C.sub.f /C.sub.s =a.sub.s, (4)
one readily finds that the quantity M, computed from sample measurements of e.sub.m and e.sub.f, equals EQU M=(C.sub.m -C.sub.f)/C.sub.f [1+a.sub.s +a.sub.s (C.sub.m -C.sub.f)/C.sub.f ] (5)
It is now further well-established based upon the work of Maxwell, Rayleigh, Landauer and Boettcher that the volume fraction .phi..sub.s of the entrained component or solid is related to the quantity (C.sub.m -C.sub.f)/C.sub.f through EQU (C.sub.m -C.sub.f)/C.sub.f =B.phi..sub.s /(1-G.phi..sub.s) (6)
where B and G are functions of the dielectric constants of the two phases, fluid and solid. Insofar as these two dielectric constants are known or can be measured, one therefore obtains a direct relation between the sample readout composite M and the solid volume fraction, EQU .phi..sub.s =M/(A.sub.o +A.sub.1 M), (7)
where EQU A.sub.o =B/(1+a.sub.s), EQU A.sub.1 =G-a.sub.s A.sub.o.
In turn, the bulk density given by Eq. (2), can be calculated from .sub.s and the known intrinsic densities of the two phases.
It follows that capacitive densitometry can satisfy the requirements specified above, in particular the requirement of absolute readout, through the combination of a capacitive device of suitable geometry and an on-line computer that is programmed to calculate M from sample values of e.sub.m and e.sub.f, and to solve Eq. (7) as well as other equations such as Eq. (2), and/or Eq. (1) when the densitometer is deployed in conjunction with a means of measuring the flow speed v.sub.f. However, as configured in existing devices, capacitive sensors have not had the capability of uniform sensing throughout the duct, especially with regard to the central concentration of solids that is found in either horizontal or vertical flow.
Other inventions have been directed at improving the accuracy of online densitometers. In U.S. Pat. No. 3,176,222 by E. A. Atkinsson, the invention shows a densitometer having a radial design in which one of the capacitor electrodes is a plug positioned in the interior of the duct by means of mounting struts. The duct wall itself is the other capacitor electrode in this design. The electric field extends radially outward from the plug which is positioned in the center of the duct to the other electrode plate which surrounds it. A disadvantage of this invention is that it requires positioning a plug and mounting struts in the flow thereby subjecting them to abrasive forces of the flow and contributing to the turbulence therein. In U.S. Pat. No. 3,635,082 by Samuel B. Prellwitz, et al., the invention addresses correction of the electric field by means of wrapping narrow electrode plates spirally around and along the duct. The narrow electrode configuration of Prellwitz samples the centerflow more strongly than the peripheral flow, therefore, introducing inaccuracies into the measurement. Furthermore, the narrowness of the plates, and their close proximity to the adjacent plates, results in a relatively weak component of capacity that senses the duct interior, and therefore, a relatively strong parasitic capacity component. This inevitably affects the accuracy of the device.
Furthermore, existing capacitive and other devices intended for online densitometry have not provided an absolute readout but instead, rely on calibration. This can be costly and difficult. For example, when the measurement site features high temperatures and pressures within the duct, then those conditions would have to be reproduced in the test loop or facility where an accurate calibration can be effected. This might require the construction of a special facility. In addition, conventional electronics, even when components of high quality are used, require recalibration as slow changes in gain, phase, supply voltage and frequency are produced by changes in capacity or resistance of circuit elements. The present invention incorporates a specific electronics scheme that, through cancellation of the above mentioned drift effects, achieves a much enhanced long-term stability.
To sum up, the online densitometer will need the following features: First, a capacitor plate geometry design that conforms to a duct of circular cross section (as usually is found in solid/fluid feedlines) yet reads the interior of the duct uniformly without producing field lines that terminate on the signal pickup electrode after passing through the outside surroundings of the duct; second, a strong signal; third, high stability for long intervals; fourth, the capability of producing an absolute measurement so that frequent direct calibration of the instrument is not needed.
It is an object of this invention to secure a highly uniform electric field within an online densitometer.
It is a further object of the invention to provide means that eliminate the possibility of electric field lines of an online densitometer from passing through the surroundings outside the medium.
It is another object of this invention to produce, through the use of online digital computation and exploitation of well-established theoretical equations, an absolute readout.
It is another object of this invention to provide a highly stable electronics scheme that also lends itself readily to online digital computation.